In 2012, infants having surgery for congenital heart disease have a high survival. The investigators are now focused on improving how sick these infants become after surgery (short term outcomes) and their later neurodevelopment (long term outcomes). During heart surgery, cardiopulmonary bypass (CPB; the heart-lung machine) takes over heart function while the surgeon repairs the heart disease. During this surgery there are periods of time when the amount of blood going to the heart and brain is lower than usual, called "ischemia". Once the surgery is finished the blood going to the heart and brain is increased to normal again, called "reperfusion". This ischemia-reperfusion can cause injury to the heart, brain, and other organs, affecting the short and long term outcomes in these infants. Adult studies have shown that a short time of ischemia to the legs for 5-10 minutes [the legs are not damaged by a short time of ischemia, unlike the heart or brain], before severe ischemia to another distant vulnerable vital organ [like the heart or brain], can protect this other vital organ from ischemia-reperfusion injury. This is called "remote ischemic preconditioning" (RIPC). Our objective is to test whether RIPC before heart surgery can improve the recovery of the heart and brain after heart surgery in newborn babies with congenital heart disease. The investigators will test whether RIPC will result in lower peak lactate and troponin levels on the day after heart surgery. Lactate levels are a marker for how much the different tissues of the body suffer from ischemia-reperfusion injury. Troponin is released from damaged heart during ischemia-reperfusion. In our trial infants will be randomized to RIPC or control. This means each baby has an equal chance of being in one group or the other. The intervention group will have RIPC before surgery; the "control group" will not. The investigators hope this trial will lead to a larger study to test if RIPC results in fewer days on a breathing machine after surgery, lower mortality, and higher scores on neurodevelopmental tests at 2 years of age.